Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in PYTHON):

Solution:
#! /usr/bin/python

import sys
import math

def check(n):
    if (n <= 0):
        return False
    #k * (k + 1) = 2 * n
    k = (-1.0 + (1.0 + 8.0 * float(n)) ** 0.5) / 2.0
    if abs(k - int(k)) < 1e-9:
        return True
    else:
        return False

n = int(raw_input())
i = 1
while (True):
    m = i * (i + 1) / 2
    if (m > n):
        break
    if check(n - m):
        print 'YES'
        sys.exit()
    i = i + 1
print 'NO'